A Sectoral Approach to News Shocks
Marija Vukotić
University of Warwick
June, 2013
Abstract
In this paper, I explore the dynamic e¤ects of aggregate news about future technology
improvements on sectoral fundamentals. I document that the durable goods sector responds
signi…cantly more to news shocks than the nondurable goods sector. By looking at the behavior of various sectoral fundamentals and also inventories, which have been largely neglected
in the news literature, I show that aggregate news propagates the business cycle mainly
through the durable goods sector. My theoretical framework is a two-sector, two-factor, real
business cycle model augmented with the following three real rigidities: habit persistence in
consumption, variable capacity utilization, and investment adjustment costs in both sectors.
In addition, I introduce inventories as a factor in the production of durable goods. The
model is successful in replicating the empirical responses of the US economy to news shocks.
It reproduces the stronger response of the durable goods sector and can perfectly match the
responses of inventories.
Keywords: News Shocks, Durable and Nondurable Goods Sectors, Inventories
JEL Classi…cation Codes: E32, D84, L60, C51
Contact Information: M.Vukotic@warwick.ac.uk; University of Warwick, Department of Economics. Gibbet
Hill Road, Coventry CV47AL. Phone: +442476128418.
1
1
Introduction
The idea that the expectations about future changes in productivity represent an important driving
force of the business cycle has received a great deal of attention in the recent literature in economics, after being abandoned for more than half a century.1 Beaudry and Portier (2004, 2006),
Christiano et al. (2010), Jaimovich and Rebelo (2009), Beaudry and Lucke (2010), and SchmittGrohé and Uribe (2012), among others, provide compelling evidence that news about future technological developments accounts for the bulk of business-cycle ‡uctuations. A di¤erent stream of
the literature investigates the role of the durable goods industries in the propagation of business
cycles. In particular, Mankiw (1985) concludes that durable goods industries play an essential
role in the business cycle and that explaining ‡uctuations in the durable goods sector is vital for
understanding aggregate economic ‡uctuations. The purpose of this paper is to link these two
ideas and analyze through which sectors news shocks propagate the business cycle.
Understanding the nature of the aggregate news shock is a crucial …rst step in my analysis since
the e¤ects of aggregate news on sectoral fundamentals obviously depend on whether aggregate news
contains information about the nondurable, durable, or both sectors. For instance, consider the
following three simple scenarios: aggregate news being news about only the nondurable sector,
about only the durable sector, or about both sectors simultaneously. In the …rst situation, an
aggregate news shock would represent a demand shock to the durable sector and a supply shock
to the nondurable sector, since investment in capital in the nondurable sector increases as a result
of higher productivity and higher consumer demand. In the second case, a news shock represents
both a supply and a demand shock to the durable goods sector, and, presumably, would imply
signi…cantly di¤erent behavior on the part of durable goods producers in response to the shock.
Finally, the third scenario represents a combination of the …rst two.
By examining the behavior of a variety of fundamentals at the sectoral level, I show that
the second scenario is the dominant one. Aggregate news appears, mainly, to be news about
productivity in the durable goods sector. Although the dynamics of all sectoral level fundamentals
are altered in the three scenarios, the behavior of investment and inventories in the durable goods
sector is helpful to revealing which of the three scenarios is most likely. In particular, my empirical
1
Pigou (1927) was one of the …rst authors to propose that agents’expectations about the future are an important
source of business cycle ‡uctuations.
2
analysis shows that the response of the inventories to a unit aggregate news shock is statistically
signi…cant; this would not be the case if the dominant scenario were the …rst one (aggregate news
being news only about the nondurable sector), since, as I show, a demand shock to the durable
goods sector would not a¤ect inventories of the durable sector in a quantitatively signi…cant way.
My analysis, therefore, con…rms that the behavior of inventories carries relevant information for
understanding the propagation of news shocks and business cycles.
To identify news shocks, I use the two-step identi…cation procedure proposed by Beaudry and
Portier (2006). This identi…cation procedure sequentially uses short-run and long-run identi…cation
schemes to recover news shocks. It assumes that news shocks are ones which are orthogonal to
current total factor productivity (TFP) innovations but permanently raise TFP in the long run.
On the other hand, news shocks represent innovations to the stock price index and therefore
instantaneously a¤ect it. Whereas Beaudry and Portier recover aggregate news shock, I recover,
in addition, sector-speci…c news shocks. Speci…cally, I retrieve news shocks for the manufacturing
sector, the durable goods sector, and the nondurable goods sector. In order to do so, I create a
data set composed of quarterly TFP (corrected for variation in capacity utilization) and stock price
indices at the level of these three sectors. To do so, I mimic the procedure utilized by Beaudry
and Portier (2006), but implement it at the sectoral level.
After obtaining measures of aggregate and sectoral news shocks, I investigate how they a¤ect
the behavior of the following sectoral fundamentals: productivity, consumption, hours, output
and investment. I show that there is a great deal of comovement among these variables at the
sectoral levels. However, the data indicate that there are much higher percentage responses of
relevant variables in the durable goods sector than in the nondurable goods sector. In particular,
after a 1 percent aggregate news shock, durable sector productivity responds by approximately
3 percent after ten quarters, while the response of productivity in the nondurable goods sector
is approximately 0.5 percent. The percentage responses of other durable goods sector fundamentals are also signi…cantly higher than those of the same fundamentals in the nondurable goods
sector. Furthermore, when I investigate the e¤ects of sector-speci…c news on the same sectoral
fundamentals this basic pattern prevails.
My results suggest that aggregate news shocks are propagated primarily through the durable
goods sector. Within the durable goods sector, the percentage responses are the highest in the
3
following two-digit standard industrial classi…cation code (SIC) industries: primary metals, industrial machinery, instruments, and electronic equipment. These are, in fact, the industries with the
highest share in the value added of the manufacturing sector in the United States. The percentage
responses of the nondurable goods sector variables are much less than those of the durable goods
sector variables; among the nondurable goods sector industries, the industries that respond the
most are those that produce goods having some level of durability, even though they are classi…ed
as nondurable industries.
My investigation of inventories is motivated by an obvious and key di¤erence between the
durable and nondurable sectors. Nearly a century ago, Pigou (1927) proposes that the possibility of holding stocks of inventories explained the fact that business cycle ‡uctuations are more
pronounced in durables industries than in nondurables industries.2 Early research in the real business cycle tradition (see Blinder (1986), Christiano and Eichenbaum (1987), Eichenbaum (1984),
Ramey (1989)) focused considerable attention on the importance of explaining the behavior of
inventories. Recent research has suggested that improved inventories management contributed to
the great moderation (see Kahn (2008a,b)). I re-establish the role and importance of inventories
with new empirical evidence concerning the response of inventories to news shocks. To do so, I
use the two standard inventories indicators: the inventories-to-sales ratio and the change in the
inventories-to-output ratio. Whereas the percentage responses of both inventories indicators to
news are statistically signi…cant in the durables sector, the percentage responses of inventories in
the nondurables sector are statistically insigni…cant.
Finally, I design a theoretical model that is consistent with the empirical evidence on how the
economy responds to news shocks. Speci…cally, I build a two-sector, two-factor, real business cycle
model which follows Baxter (1996) in its basic structure. Sector 1 produces a pure consumption
2
In his book Industrial Fluctuations, Pigou says the following: "When for any reason the aggregate demand is
increased in commodities that are durable and are not destroyed in the act of use, the resultant extra production of
these commodities in the years of high demand involves the existence of a correspondingly enlarged stock, and so
gives rise to a smaller demand for new production of these commodities than it used to give rise to before. Thus, the
upward ‡uctuation of industrial activity above the normal carries with it a subsequent downward ‡uctuation below
the normal when the stimulus is removed, and not merely a subsequent return to the normal... The same thing
holds good of those consumption goods which are destroyed in a single act of use, provided that they are durable
in their own nature and are of such a sort that they can be held in store without great cost of risk: for dealers pile
up stocks of them in booms, and in depressions are forced to o¤er them out of their stocks in competition with the
current output of industry... Here, then, we have a second reason for expecting that instrumental industries will
‡uctuate more than others, even though it is in the others that the cause of ‡uctuations lies."
4
(nondurable) good, whereas sector 2 produces consumer durables and the capital good used in
producing both goods. Both sectors use capital and labor as their factor inputs. The key di¤erence
between the two sectors is that a good produced in sector 2 can be stocked, whereas the output
of sector 1 is perishable. I model this feature by adding inventories into the production function
of sector 2, following Christiano (1988) and Kydland and Prescott (1982). These authors argue
that the stock of inventories, as the stock of …xed capital, provides a ‡ow of services to a …rm.
My model is augmented by the following four real rigidities: habit persistence in consumption,
investment adjustment costs in both sectors, as well as adjustment costs associated with changes
in the stock of consumer durables, and variable capacity utilization. I introduce habit persistence
in consumption in order to obtain a hump-shaped consumption response. Following Jaimovich and
Rebelo (2009), I introduce investment adjustment costs in order to obtain comovement between
hours, consumption, output and investment. Variable capacity utilization assures that the modelbased and empirical measures of TFP coincide. Finally, news shocks are introduced by feeding
the empirical responses of TFP in the two sectors into the model.
The model is successful in mimicking the empirical responses to news shocks at the sectoral
level. First, the response of the inventories-to-sales ratio can be perfectly matched. Second, the
model is able to reproduce the stronger overall response of the durable goods sector to news shocks.
For example, responses of hours, consumption and output are all higher in the durable goods sector.
Third, the model reproduces the comovements observed among sectoral level fundamentals. That
is, the model reproduces comovement among hours, consumption, output and investment in both
sectors. Even though it cannot perfectly match the responses of all the variables (for example,
response of hours in the nondurable goods sector), overall the model …ts the data rather well.
The remainder of the paper is structured as follows: In Section 2, I describe some of the
main …ndings in more detail, the data used in the analysis, as well as all empirical …ndings. In
particular, I …rst explain how I obtain measures of aggregate and sectoral news shocks and how
I recover their e¤ects on sectoral fundamentals. The two-sector model is presented in Section 3.
Section 4 explains calibration and estimation of the model. Quantitative …ndings using the model
are presented in Section 5. Section 6 concludes.
5
2
Empirical Evidence
In this paper, I investigate, analyze and de…ne the nature of aggregate news shocks. I …rst explore
the e¤ects of aggregate news shocks on sectoral TFPs and stock price indices. Speci…cally, I
analyze the manufacturing sector, the durable goods sector, and the nondurable goods sector (see
responses in Figure 1). According to the analysis, whereas TFPs do not respond immediately to
news, stock prices do in all sectors. This observation con…rms that news is immediately re‡ected
in the variables that express agents’expectations about the future, such as stock prices. Another
striking observation is the di¤erent quantitative behavior of durable and nondurable goods sectors.
Both the percentage responses of TFP and stock prices in the durable goods sector are signi…cantly
greater than in the nondurable goods sector. Speci…cally, after ten quarters, the response of durable
sector TFP is almost …ve times greater than the response of nondurable sector TFP, whereas the
impact response of the durable sector stock price index is 2 percent greater than the impact
response of the nondurable sector stock price index. This might suggest that the information
contained in an aggregate news shock is more about future productivity in the durable sector than
about nondurable sector productivity.
Figure 1: Impulse responses of the sectoral TFPs and Stock Price Indices to
a unit aggregate news shock
Note: Impulse responses of sectoral TFPs to a unit aggregate news shock are given in the left panel;
the responses of sectoral stock price indices are given in the right panel. Shaded areas represent 5% and
95% con…dence bands of the responses at the level of the manufacturing sector, which are obtained using
the Monte-Carlo experiments with 1000 replications.
A key di¤erence between durable and nondurable producers is that the former are more able
6
to respond quickly to demand shocks by running down stocks of inventories.3 My exploration of
the role of inventories, which have not previously been studied in the news literature, is motivated
by this key di¤erence between the producers of durable and nondurable goods. My empirical
evidence suggests that the response of inventories-to-sales ratio to an aggregate news shock is
almost nonexistent in the nondurable industries, whereas there is a noticeable and signi…cant
drop in the durable industries. The average responses of the inventories-to-sales ratio in the
manufacturing, durable, and nondurable sectors are presented in Figure 2. Speci…cally, in the
durables sector the ratio drops by 0:4 percent within one year of a news shock, whereas the
average response in the nondurables sector is small and insigni…cant.
Figure 2: Impulse response of the sectoral inventories to sales ratio to a
unit aggregate news shock
Note: Point estimates of the responses of manufacturing, durables and nondurables sector inventories
to sales ratio to a unit aggregate news shock are displayed. Shaded areas represent 5% and 95% con…dence
bands of the responses at the level of the manufacturing sector, which are obtained using the Monte-Carlo
experiments with 1000 replications.
In order to achieve a more complete analysis, I extend my investigation to other sectoral-level
fundamentals, such as hours, output, investment, and consumption. A discussion of this follows a
detailed explanation of how aggregate news shock and sectoral news shocks are identi…ed.
3
This is not to say that stocks of inventories cannot be held in the nondurable sector industries, but their
volume is lower than in the durable sector industries. In particular, more than 60 percent of manufacturing sector
inventories are carried by the durable sector. Also, the inventories of durable producers can be held for a longer
periods of time.
7
2.1
Identi…cation of News Shocks
When the e¤ects of a particular shock are discussed in macroeconomics, an important …rst step
is to clearly communicate the validity of the identi…cation scheme. News shocks are typically
de…ned as the arrival of new information about future productivity growth that ends up being
re‡ected instantaneously in forward-looking variables, but does not have an instantaneous impact
on the current TFP.4 Rather, the e¤ects on TFP are realized only after a certain number of quarters. Although it is relatively straightforward to think about this phenomenon in the theoretical
framework, recovering its empirical analog is more challenging. In this paper, I will use the identi…cation scheme proposed by Beaudry and Portier (2006). There are other identi…cation schemes
proposed in the literature as well. For example, Barsky and Sims (2011) identify news shock as
a shock orthogonal to the TFP innovation that best explains future variation in measured TFP.
Although news identi…ed using this identi…cation scheme does not reproduce comovement among
consumption, hours, output and investment, it still leads to larger responses in the durable sector.
However, the purpose of this paper is not to propose a new identi…cation scheme, and therefore I
choose one identi…cation strategy to carry out my analysis.
The identi…cation procedure of Beaudry and Portier takes, as a starting point, the de…nition
of a news shock given above. The most natural choice of variables on which to base the procedure
are a measure of productivity and some forward-looking variable that contains information about
future developments. Like Beaudry and Portier, I use TFP as the measure of productivity, and
a stock price index as the forward-looking variable. I start with a bivariate time series model for
these variables. In order to recover news shocks, I sequentially impose two separate identi…cation
restrictions, described as the short-run and long-run, on the model.
To describe the short-run restriction, I assume that the two variables can be represented in log
…rst di¤erences, by the Wold representation:
2
where
4
(L) =
P1
i=0
4
i
iL ;
T F Pt
SPt
3
2
5 = (L) 4
"1t
"2t
3
5
and the two shocks, "1t and "2t ; are mutually orthogonal and have unit
See, for example Beaudry and Portier (2006), Christiano et al. (2010), Jaimovich and Rebelo (2009).
8
variance. The short-run restriction imposes that "2 , has no short-run e¤ect on TFP. More formally,
this restriction is imposed by setting the 1; 2 element of the matrix
0
to zero.
The long-run restriction is based on an alternative Wold representation
2
4
T F Pt
SPt
3
2
5 = e(L) 4
e
"1t
e
"2t
3
5
P e i
where e (L) = 1
"1t and e
"2t ; are mutually orthogonal and have unit
i=0 i L ; and the two shocks, e
variance. The long-run restriction is that only e
"1t , has a long-run e¤ect on TFP. This restriction
P e i
5
is imposed by setting the 1; 2 element of the matrix e (L) = 1
i=0 i L to zero.
As such these two identi…cation schemes are purely ad-hoc. However, suppose that it happens
to be the case that the two recovered disturbances, "2 and e
"1 , are extremely highly correlated,
or e¤ectively the same. This suggests that the procedure has recovered a single shock that, since
it satis…es the short-run restriction, does not have an immediate e¤ect on the productivity and
a¤ects it only with a delay, and, since it satis…es the long-run restriction, captures all important
long-run information about productivity. Given these characteristics, the shock satis…es the two
characteristics of news described above. Of course, the procedure only delivers plausible measures
of news if the two shocks happen to be highly correlated.
2.2
Data
The data used in this paper can be broadly divided into aggregate and sectoral-level series. Specifically, I use data from the manufacturing which allow me to distinguish between the durable and
nondurable goods sectors. As a further level of disaggregation, I also use data on nineteen two-digit
SIC code manufacturing industries. Data for the manufacturing, durable goods, and nondurable
goods sectors are available at the quarterly frequency for the sample period 1972:I - 2007:IV. Data
for the two-digit industries are also available at the quarterly frequency, but for a shorter sample
5
If the two series are found to be cointegrated, all elements in the second column equal zero, i.e. e
"1 is the only
permanent shock. This is because the rank of the matrix is one in the presence of the one cointegrating relation.
Hence, in this case, a simple Cholesky decomposition cannot be used to recuperate the structural news shock,
as in Blanchard and Quah (1989). In fact, to recover disturbance e
"1 , I follow the procedure proposed by King
et al. (1991). This procedure allows one to impose the long-run restrictions using the fact of the existence of the
cointegrating relations.
9
period, 1972:I - 1997:III.6 Finally, aggregate data, for the entire US economy, are available at the
quarterly frequency for the period 1949:I - 2007:IV.
In order to recover news shocks at all levels of aggregation, I create a data set composed of
TFP and stock prices for these three sectors and nineteen two-digit industries. I construct TFP
following Burnside, Eichenbaum and Rebelo (1995). Rather than considering their three di¤erent
technology speci…cations, I use the model that allows me to measure TFP at the two-digit level,
despite the absence of observations on material inputs. Speci…cally, I assume that time t gross
output is produced using a Leontief production function
Yt = min (Mt ; Vt ) ;
where Mt denotes time t materials and Vt denotes value-added at time t, which, itself, is produced
using hours of work (Nt ) ; the stock of capital (Kt ), and time varying capital utilization, measured
by electricity use (Et ) : As Burnside, Eichenbaum and Rebelo show, this speci…cation allows gross
output in sector i to be written as
Yti = Ait F
where
Nti ;
Eti
;
represents the assumed …xed proportion between electricity consumption and capital
services, with the latter being the product of the capital stock and its work week. I further assume
that the function F ( ) takes the Cobb-Douglas form.
After assuming that the labor and electricity markets are perfectly competitive, the expression
for TFP in a sector or industry i can be obtained using a …rst-order log-linear approximation of
the production function:
Yti = (1
where
1)
Nti +
Ait is assumed to be the growth rate of TFP,
6
1
Eti +
Ait ;
Yti the growth rate of output,
(TFP)
Nti the
In 1997 the SIC was replaced by the North American Industry Classi…cation System (NAICS), and it is not
possible to extend the two-digit SIC series further than 1997. Also, historical data have not been transformed to
match NAICS.
10
growth rate of labor input and
Eti the growth rate of electricity use in sector or industry i.7
Data on output (measured using the relevant indices of industrial production) and electricity
consumption (my proxy for capital services) at the sectoral level are obtained from the Federal
Reserve Board. As emphasized by Beaudry and Portier (2006) and Barsky and Sims (2011),
TFP measures that are adjusted for capacity utilization are preferable since they lead to more
realistic, substantially delayed, productivity responses to news shock. As a sectoral labor measure,
I use the quarterly averages of monthly production workers, which is constructed as the product
of the following two time series: average weekly hours of production workers and the number of
production workers, both obtained from the Bureau of Labor Statistics. Finally, my assumption of
a constant returns to scale Cobb-Douglas technology allows me to calibrate the parameter 1
1,
using labor’s share of income.8 I compute labor’s share as the ratio of labor compensation and
nominal income in each sector or industry. Both series needed for this calculation are obtained
from the Bureau of Economic Analysis.
Sectoral stock price data are extracted from Kenneth French’s website.9 Data on S&P500 were
obtained from Robert Shiller’s website.10 Using the consumer price index (CPI) as the in‡ation
measure and the civilian noninstitutional population over 16, I convert these data to real per capita
measures. Besides using TFP and stock price indices data in my empirical analysis, I also use
data on real per capita consumption, hours, investment, output and several inventories indicators,
at the aggregate and sectoral level. Detailed explanations of these data and all other data used in
the paper, as well as their sources, are provided in the online Appendix A.
7
Since in my model I consider inventories to be a factor of the production in the durable goods sector, the durable
dur
sector measure of TFP will be slightly altered in order to account for this: Adur
= Ytdur
1
Ntdur
t
dur
dur
dur
dur
(1
) Et
It ; where controls for the role of inventories It in the production function of
the durable goods sector.
8
Burnside (1996) concludes that "the typical U.S. manufacturing industry displays constant returns with no
external e¤ects."
9
The data are available for download at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_lInibrary.html.
The data are constructed from The Center for Research in Security Prices (CRSP) database. The particular series
used here are the stock price indices of the manufacturing sector, durable goods sector, nondurable goods sector,
as well as stock price indices of all two-digit SIC manufacturing industries.
10
Available at http://www.econ.yale.edu/~shiller/data.htm
11
2.3
Sectoral News
The news literature has focused primarily on aggregate news and its e¤ects on aggregate variables,
and has remained largely silent concerning the e¤ects of news on sectoral fundamentals, and
concerning the possibility that some shocks are in fact news speci…c to a particular sector of
the economy. In order to understand these sectoral aspects of news shocks, in this section I
describe news shocks recovered at the sectoral level, and I explore the dynamic responses of
sectoral fundamentals to aggregate and sector-speci…c news.
Beaudry and Portier (2006) show that, for the aggregate US economy, the two disturbances,
"2t and e
"1t , obtained from the short-run and long-run identi…cation schemes are highly correlated,
and induce nearly identical dynamic responses of TFP and stock prices. This feature of the
identi…ed shocks is preserved when a third variable, such as consumption, output, investment, or
hours is added to the system. More importantly for my analysis, the correlation between the two
disturbances is very high also when sectoral data is used. In particular, I identify news shocks
in the manufacturing, durable goods and nondurable goods sectors and compare these recovered
sectoral level shocks to the aggregate news shocks. Manufacturing news shock is identi…ed using a
two-variable vector autoregressive system in the log …rst di¤erences of TFP and stock price index
for the manufacturing sector. According to a Likelihood Ratio Test, the hypothesis of cointegration
between TFP and the stock price index cannot be rejected at the 5% level.11 Therefore, a vector
error correction model (VECM) is the appropriate speci…cation. In the case of the manufacturing
sector, the correlation between the two identi…ed disturbances, "2 (short-run) and e
"1 (long-run) ;
is very high, 0:994.
The responses of the manufacturing sector TFP and stock price index to a 1 percent increase
in "2 and e
"1 are displayed in Figure 3. As in the aggregate economy, the dynamics induced by
the two disturbances are very similar. In particular, the short-run disturbance, "2 ; permanently
a¤ects TFP while the long-run disturbance, e
"1 ; has nearly no impact e¤ect on TFP. These two
facts suggest that the identi…cation procedure has correctly isolated news shocks in the manufac-
turing sector. The impulse response functions for TFP have a somewhat di¤erent shape in the
manufacturing sector than they do for the full economy. In the aggregate case, TFP increases soon
after the shock, and does so sharply, whereas manufacturing sector TFP increases slowly after an
11
See (Hamilton, 1994, p. 648).
12
initial (statistically insigni…cant) drop in the …rst two quarters after the shock.12 The response of
the manufacturing stock price index is very similar to the response of its aggregate counterpart
to aggregate news. It increases on impact by 7:5 percent and remains at roughly the same level
inde…nitely.
Figure 3: Impulse responses to shocks "2 and e
"1 in the (TFP, SP) VAR at the
manufacturing sector level
Note: Left panel represents the response of the manufacturing TFP to the two disturbances; the
response of the manufacturing stock price index to these disturbances is given on the right panel. Dotted
lines represent point estimates of the responses to a unit "2 shock, solid lines represent the responses to
a unit e
"1 shock, whereas the borders of the shaded area represent 5% and 95% con…dence bands of the
impulse response functions in the case of long-run identi…cation. Con…dence bands are obtained using
the Monte-Carlo experiments with 5000 replications.
I also identify durable-sector-speci…c news shocks and nondurable-sector-speci…c news shocks
by adopting the same identi…cation procedure. I use a two-variable VECM in the log …rst di¤erences of sectoral TFP and stock prices for the durable and nondurable goods sectors respectively.13
Figure 4 displays the impulse response functions of sectoral TFPs and stock prices.
12
Nevertheless, when aggregate TFP is corrected for capacity utilization, its qualitative response more closely
resembles the response of the manufacturing TFP response. In particular, aggregate TFP does not increase for
several years; the di¤usion process appears to be slower than when unadjusted measure of TFP is used.
13
In both sectors, a Likelihood Ratio Test suggests the presence of one cointegrating vector.
13
Figure 4: Impulse responses to shocks "2 and e
"1 in the (TFP, SP) VAR at the
durables sector level (the upper panel) and nondurables sector level (the
lower panel)
Note: The top panel represents the responses of the durable goods sector TFP and stock price index,
whereas the lower-panel represents the responses of the nondurable goods sector TFP and stock price
index. On both panels, left graph represents the responses of TFPs to the two disturbances, whereas the
right graph represents the responses of SP to these disturbances. Dotted lines represent point estimates
of the responses to a unit "2 shock, solid lines represent the responses to a unit e
"1 shock, whereas the
borders of the shaded area represent 5% and 95% con…dence bands of the impulse response functions in
the case of long-run identi…cation. Con…dence bands are obtained using the Monte-Carlo experiments
with 5000 replications.
As in the case of the aggregate economy and manufacturing sector, the disturbances originating
from the short-run and long-run identi…cation procedures induce quite similar dynamics. However,
in both sectors, the long-run shock, e
"1 ; has an immediate e¤ect on TFP; in the durable sector it
rises by approximately 2 percent, whereas in the nondurable sector it rises by 1 percent. But, as
the time horizon expands, the two responses almost converge in both sectors. Furthermore, the
14
two responses lie within the 95% long-run con…dence bands, suggesting statistical similarity.
Evidently, the long-run response of durable sector TFP is considerably greater than that of
nondurable goods sector TFP; after 40 quarters, the e¤ect of a 1 percent durable sector news shock
on durables TFP is approximately 4 percent, whereas the e¤ect of a 1 percent nondurable sector
news shock on nondurables TFP is less than 1 percent. This greater response of durables TFP
suggests that the relatively large 1:5 percent response of manufacturing TFP to a news shock is
mostly driven by the behavior of the durable sector. In addition, the response of durables TFP to
durables news qualitatively resembles the response of its manufacturing counterpart to manufacturing news. Both the higher durables TFP response and its resemblance to the manufacturing
TFP response suggest that manufacturing news is mainly about the future growth of durables
TFP, rather than about the future growth of nondurables TFP.
Even though the long-run disturbances have an immediate e¤ect on sectoral TFPs, the correlations between the two disturbances in both sectors are still high (0:934 in the durable goods
sector and 0:989 in the nondurable goods sector). Scatter plots of the two disturbances, "2 and
e
"1 ; at the manufacturing, durables, and nondurables levels are plotted in Figure 5.
Figure 5: Correlation between "2 and e
"1 in the Manufacturing, Durable and
Nondurable Goods Sectors
Note: Two disturbances, "2 and e
"1 ; are plotted against each other at the level of the manufacturing
sector, durable goods sector and nondurable goods sector.
In order to understand how these aggregate and sectoral news shocks are related, I calculated
correlations between aggregate news shocks and sectoral news shocks. The correlation between
the aggregate and nondurable news shocks (0:738), is lower that the correlation between the aggregate and durable news shocks (0:758). This result also holds when manufacturing news is
15
compared to durable and nondurable news; the correlation between the durables and manufacturing news is 0:885, whereas the correlation between the nondurable and manufacturing news
shocks is 0:837. These facts indicate that aggregate and manufacturing news shocks carry more
information concerning the durable sector developments, than they do concerning the nondurable
sector.
In order to investigate whether the higher durable sector responses are due only to some
aggregation e¤ect, in the next section I extend the analysis to a more disaggregated level. I
consider two-digit SIC industries and their responses to various types of news shocks.
2.3.1
Two-digit SIC Level
The same identi…cation procedure is performed at the level of nineteen two-digit SIC manufacturing industries.14 Speci…cally, ten of these industries are classi…ed as durable goods industries, and
the remaining nine as nondurable goods industries. For each two-digit SIC industry, I construct
a vector autoregressive system composed of the TFP and stock price index of that particular industry, sequentially performing short-run and the long-run identi…cations. However, at the more
disaggregated level, impulse response functions implied by the two disturbances follow rather different dynamics, contrary to the aggregate or sectoral levels. Thus, the correlation between the
two recovered shocks is rather small, on average. This evidence suggests that the identi…cation
scheme fails to recover news shocks that are speci…c to the two-digit SIC industries. One plausible
explanation is that classifying …rms according to two-digit SIC codes is somewhat di¢ cult. In
particular, SIC classi…es establishments by their primary type of activity - the activity that contributes the most to the value added of the establishment. Since …rms often operate in more than
one industry, the information that is contained in their TFP or stock price index is not necessarily
tied to only one two-digit SIC industry. Hence, as the level of disaggregation deepens, it becomes
more di¢ cult to extract industry-speci…c news shocks from the data.
Even though I am not able to identify news speci…c to the two-digit SIC industries, the behavior
of the two-digit SIC productivity, stock prices, and other fundamentals in response to recovered
aggregate or sectoral news may carry important information. Conditional upon the recovered
14
SIC represents a numerical system developed by the Federal Government for classifying all types of economic
activity within the United States economy.
16
shocks representing news shocks, one can run the following regression:
Xt =
J
X
j "2;t j
+
t;
(1)
j=0
in order to infer the e¤ects of news shocks on a variable Xt . Here, "2t represents the recovered
structural news shock at time t coming from the short-run identi…cation procedure.15 Speci…cally,
it can represent either the aggregate news shock or one of the three recovered sectoral news shocks.
The point estimate impulse response of variable Xt to a particular news shock after a horizon n
P
is measured as the cumulative sum of the regression coe¢ cients 0j s : nj=1 j :
I …rst investigate the e¤ects of an aggregate news shock on the productivity of the nineteen
two-digit SIC industries. Figure 6 displays the responses of durables and nondurables industries
to a unit aggregate news shock. First, the impact response of productivity is statistically equal
to zero in all industries, satisfying the condition that news shocks do not a¤ect productivity
immediately. Second, durables industries are, on average, more responsive to aggregate news in
the long-run than nondurable industries. Within the durable goods sector, industries with the
highest percentage responses are the following: primary metals, industrial machinery, instruments
and electronic equipment. These industries have the highest shares in the total value added of
the durable goods sector. On average, the responses in the nondurable sector industries are much
smaller. Industries that consistently respond the most, among the nondurable goods industries,
are chemicals, petroleum, and textile mills, which are industries whose output has a somewhat
durable character.16
When I repeat a similar exercise - recovering industry responses to sectoral news - I obtain
similar conclusions. First, durable goods industries respond more to all types of news shocks.
Second, the response of each two-digit SIC industry is the highest to a news shock speci…c to
the sector to which the industry belongs (according to the SIC). For instance, nondurable goods
industries respond more to nondurable news shocks than to durable news shocks, whereas durable
15
Since I showed that the correlations between the long-run and short-run shocks are very high (both at the
aggregate and sectoral levels), the e¤ects of ~"1 and "2 on Xt are nearly identical:
16
Beaudry and Portier (2005) use annual Multifactor Productivity Trends sectoral data in order to analyze the
e¤ects of aggregate news shocks on two-digit SIC industries. They also …nd higher responses in the durables sector.
In particular, they …nd that the industries with the highest growth rate among the durable sector industries are
those with the highest long-run responses to the aggregate news.
17
goods industries respond more to durable news shocks than to nondurable news shocks. This
result is somewhat expected, since the sector-speci…c news carries more information about the
TFP in that particular sector than, for example, aggregate news.
Figure 6: Responses of Two-Digit SIC Durables (left panel) and Nondurables
0
Industries (right panel) TFPs to a Unit Aggregate News Shock
After documenting that aggregate and sectoral news do not have an impact e¤ect on TFP in
the two-digit industries, I also examine the responses of the two-digit SIC stock price indices. If
the price indices rise on impact this supports the view that the recovered shocks represent news.
The responses of stock prices in the nineteen two-digit manufacturing industries to a 1 percent
aggregate news shock are shown in Figure 7. Stock prices respond signi…cantly on impact in
each industry, con…rming that news shocks are immediately re‡ected in forward-looking variables.
The average response of the stock price indices in the durable goods sector is higher than that of
the stock price indices in the nondurable goods sector. Speci…cally, stock prices of each durable
sector two-digit industry respond by more than 7 percent to an aggregate news shock, whereas
the response in four nondurable goods industries is less than 7 percent. The initial large response
of stock prices is followed by decreases during the following ten quarters. To explain this decline,
Haertel and Lucke (2008) argue that by the time new technology is di¤used, competition reduces
pro…ts and stock prices adjust to a lower level.
18
Figure 7: Responses of Two-Digit SIC Durables (left panel) and Nondurables
0
Industries (right panel) Stock Prices to a Unit Aggregate News Shock
2.4
E¤ects of News on Other Sectoral Fundamentals
As previously shown, the percentage response of durable goods sector TFP to news is signi…cantly
larger than that of nondurable goods sector TFP. In particular, the long-run durable sector TFP
response is almost …ve times greater than the response of the nondurable sector TFP. In order to
complete the empirical analysis, I explore whether this result is also present in the case of other
sectoral fundamentals. Speci…cally, I examine the responses of sectoral output, consumption,
hours, and investment.
Figure 8 displays the responses of sectoral fundamentals to a 1 percent aggregate news shock.
The shaded area represents 90% con…dence bands of the manufacturing sector responses. There
are several features worth noticing. First, there is evidence of the comovement among the sectoral
fundamentals. Second, the responses of all durable sector fundamentals are signi…cantly greater
than the responses of nondurable sector fundamentals. Speci…cally, after ten quarters, the percentage response of durable sector output is four times higher than that of nondurable sector output.
Also, the responses of durable consumption, hours and investment are higher than those of the
same variables in the nondurable goods sector. Third, only consumption responses are statistically positive on impact, whereas the impact responses of other fundamentals are not statistically
di¤erent from zero. After ten periods, all durable sector fundamentals remain above their initial
levels and these responses are statistically di¤erent from zero. In contrast, in the nondurable
19
goods sector only the responses of hours and output are signi…cantly di¤erent from zero after 10
quarters; the responses of consumption and investment are not statistically signi…cant over this
time horizon.
I also examine the e¤ects of sectoral news on the same sectoral fundamentals. In line with the
previous results for TFP, the e¤ects of sectoral news on sectoral fundamentals are larger than the
e¤ects of aggregate news. In particular, durable goods sector fundamentals respond most to the
durable news shock, while nondurable goods sector fundamentals respond most to the nondurable
news shock.
Figure 8: Responses of the sectoral fundamentals to a unit aggregate news
shock
Note: Solid lines represent point estimates of the sectoral responses to a unit aggregate news shock.
Shaded areas represent 5% and 95% con…dence bands of the responses at the level of manufacturing
sector.
Finally, since I document an overall larger response of durable sector TFP to aggregate news
shock, there is an implied increase in the relative productivity of the durable and nondurable goods
sectors. Hence one would expect a decline in the relative price of durables goods in response to an
aggregate news shock. Furthermore, if consumption for both types of goods occurs on impact, due
20
to a positive wealth e¤ect, the lack of inventories of nondurables could create a scarcity e¤ect that
would reinforce the decline in the relative price of durables. When I analyze the response of the
relative price of durable goods (the ratio between durable sector and nondurable sector consumer
price indices) to an aggregate news shock, the above intuition turns out to be correct. As Figure
9 displays, the relative price of durable goods decreases by 0:8 percent after ten quarters.
Figure 9: Impulse responses of the inventories-to-sales ratio to a unit
sectoral news shock
Note: Solid lines represent point estimates of the relative price of durable goods to a unit aggregate
news shock. Shaded areas represent 5% and 95% con…dence bands.
Overall, the evidence presented in this section further supports the idea that durable goods
sector fundamentals are more responsive to news shocks, and that aggregate news shocks propagate
business cycles mainly through the durable goods sector.
2.5
Inventories
A key di¤erence between durable and nondurable goods is that producers of durables can stock
inventories and use them as a bu¤er to news shocks. This feature of durable goods has potentially
important implications for how the sector responds to news shocks. For this reason, I devote
this section to examining the behavior of the two most commonly used inventories indicators: the
21
inventories-to-sales ratio and the change in the inventories-to-output ratio (see Blinder and Fischer
(1981) and Lovell (1961)). To obtain the responses of these variables to news shocks, I add the
inventories indicator to the benchmark two-variable system. When the third variable is added,
the identi…cation process becomes more involved.17
Figure 10: Impulse responses of the inventories-to-sales ratio to a unit
sectoral news shock
Note: Left panel represents the response of the manufacturing inventories-to-sales ratio to the two disturbances coming from the three-variable (TFP, stock price index, inventories-to-sales ratio) VECM at the
manufacturing sector level. Middle panel represents the response of the durables inventories-to-sales ratio
to the two durable sector disturbances originating from the three-variable VECM at the durable goods
sector level. Right panel represents the response of the nondurable inventories-to-sales ratio to the two
nondurable sector disturbances originating from the three-variable VECM at the nondurable sector level.
In all three panels the dotted lines represent the point estimates of the response to the short-run sectoral
disturbance, whereas the solid lines represent the point estimates of the responses to the long-run sectoral disturbance. Finally, shaded areas represent 5% and 95% con…dence bands of the long-run sectoral
responses. Con…dence bands are obtained using the Monte-Carlo experiments with 5000 replications.
Figure 10 displays the responses of inventories-to-sales ratio in three sectors (manufacturing,
durables, and nondurables) to the sectoral level news shocks in those sectors (identi…ed with
either the short-run or long-run restriction). The view commonly accepted in the literature is that
inventories-to-sales ratio is countercyclical.18 Firms accumulate their inventories when demand is
weak, and liquidate them when demand is high. Also, if there is uncertainty about the sales in
the future, …rms may hold inventories against the contingency that demand will be unexpectedly
17
A detailed explanation is provided in the online Appendix C.
For example, Blinder (1981) argues: "The most commonly used indicator of the state of inventory equilibrium
or disequilibrium is the ratio of inventories to sales in manufacturing and trade. This ratio moves countercyclically,
rising in recessions."
18
22
high. Therefore, one would expect the inventories-to-sales ratio to decrease when good news about
future productivity arrives. My analysis con…rms this view. Speci…cally, the inventories-to-sales
ratio in manufacturing decreases by 0:25 percent over six quarters, remaining at that level in the
longer run. As expected, the response of inventories in the durables sector is twice as large as
that in the manufacturing sector (a decline of almost 0.6 percent), whereas the response of the
inventories-to-sales ratio in the nondurables sector is statistically insigni…cant over the whole time
horizon
Figure 11: Response of the change in the inventories-to-output ratio to a unit
sectoral news shock
Note: Left panel represents the response of the change in inventories-to-output ratio in the manufacturing sector to the two disturbances originating from the three-variable (TFP, stock price index,
change in inventories-to-output ratio) VECM at the manufacturing sector level. Middle panel represents
the response of the durables change in inventories-to-output ratio to the two durable sector disturbances
(originating from the three-variable VECM at the durable goods sector level). Right panel represents
the response of the nondurable change in inventories-to-output ratio to the two nondurable sector disturbances (originating from the three-variable VECM at the nondurable goods sector level). In all three
panels the dotted lines represent the point estimates of the response to the short-run sectoral disturbance, whereas the solid lines represent the point estimates of the responses to the long-run sectoral
disturbance. Finally, shaded areas represent 5% and 95% con…dence bands of the long-run sectoral
responses. Con…dence bands are obtained using the Monte-Carlo experiments with 5000 replications.
Figure 11 displays the corresponding responses of the change in the inventories-to-output ratio.
After an initial decrease, this indicator increases, reaching a peak after …ve to six quarters. Although the response is signi…cant at the level of manufacturing and durable sector, there is, again,
no statistically signi…cant response in the nondurable sector. The rationale behind this qualitative response is as follows: as the good news about the future productivity is realized, producers
23
decrease the inventories levels in order to meet increased demand. However, as time passes, they
increase production and inventories levels return to some optimally determined, long-run level of
inventories. This indicator is not permanently a¤ected by the news, but this is explained by the
fact that it measures the change in inventories (scaled by output) as opposed to the level.
2.5.1
Inventories at the two-digit SIC level
After documenting that inventories respond much more in the durables sector than in the nondurables sector, I investigate in which two-digit industries inventories respond the most to news
shocks, and explore whether these coincide with the industries whose productivities respond most
to news shocks. In Figure 12, I present the responses of the inventories-to-sales ratio at the twodigit SIC level, to a unit aggregate news shock. The responses of both durable and nondurable
sector industries are presented.
FIGURE 12: Response of Inventories-to-Sales Ratios to a unit Aggregate News
Shock at the Level of 2-Digit SIC Industries
The percentage responses of the inventories-to-sales ratios of durable sector industries are
much larger than those of nondurable sector industries. Results are robust when sectoral news
shocks are used instead of aggregate news shocks. Again, durable goods industries are more
responsive than the nondurable goods industries. The responses of durables industries are largest
with respect to durable news, just as the responses of nondurables industries are greatest with
respect to nondurable news. Responses of all industries, on average, are larger in the case of a
unit manufacturing news shock than in that of a unit aggregate news shock. Additionally, the
24
percentage responses of durable sector inventories are higher, on average, in the case of a unit
durable news shock than in the case of a unit manufacturing news shock. Nondurable goods
inventories do not respond signi…cantly to any of the news shock, with one exception: petroleum
inventories respond signi…cantly to nondurable news shock. On the other hand, the responses of
several durable goods industries are statistically signi…cant. Finally, the durable industries with
biggest declines in inventories are the same as those with the largest responses of productivity
to news. At …rst, this result might seem surprising. If the increased demand for goods, as a
result of the wealth e¤ect, were distributed evenly across industries, then one might expect the
sectors with the biggest TFP responses to be more able to meet demand without running down
inventories. But there are two important considerations that work against this argument. First,
the di¤erent responses of TFP in the di¤erent sectors imply changes in relative prices. Industries
with larger TFP responses will have falling relative prices and there will be substitution towards
their products. Second, news about productivity leads to an increase in investment demand that,
in the short run, should put additional pressure on inventories in the durables sector but not in
the nondurables sector.
3
The Model
I use a two-sector, two-factor, real business cycle model as a theoretical framework to study sectoral
business cycles. As in Baxter (1996), sector 1 produces a nondurable consumption good, and sector
2 produces a consumer durable good and the capital good used as an input in the production of
both sectors. The main di¤erence between the two sectors is that a good produced in sector 2 can
be stocked. In the model, the reason that durable goods are held as stocked inventories, is that
inventories are an argument of the production function of sector 2, following Christiano (1988)
and Kydland and Prescott (1982). These authors argue that the stock of inventories, as the stock
of …xed capital, provides a ‡ow of services to a …rm.
3.1
Households
The economy is populated by a large number of identical, in…nitely-lived agents who derive utility
from the consumption of the nondurable consumption good, the service ‡ow from the durable
25
consumption good, and leisure. The agent’s lifetime utility is
U = E0
1
X
hCt
Ct
t
1
t=0
where
Nt )
1
1
;
represents a subjective discount factor, h is the coe¢ cient of habit persistence in con-
sumption,
Ct
v (1
1
hCt
is the inverse of the elasticity of intertemporal substitution de…ned in terms of
1
v (1
Nt ), and where Nt represents hours worked at time t. Two types of prefer-
ences are considered: preferences proposed by Greenwood, Hercowitz and Hu¤man (1988), which
I refer to as GHH; and preferences proposed by King, Plosser and Rebelo (1988), which I refer
to as KPR.19 In the case of GHH preferences, utility function is separable in consumption and
leisure, taking the following form:
U
GHH
= E0
1
X
Ct
t
hCt
Nt
1
1
1
1
t=0
:
In the case of KP R preferences, utility is given by
U
KP R
= E0
1
X
t
Ct
hCt
1
1
Nt
1
t=0
1
1
:
The composite consumption good (Ct ) is given by the constant elasticity of substitution function:
Ct = [
1 C1t
+
2 C2t ]
1
;
where C1t and C2t represent period t consumption of the nondurable consumption good and
consumption of the service ‡ow from the durable consumption good, respectively, and parameters
1
and
2
parameter
determine the weight of these two goods in the composite consumption good. The
is equal to (1
1=%) ; where % is the constant elasticity of substitution between C1t
19
Jaimovich and Rebelo (2009) show that these two types of preferences induce qualitatively di¤erent responses
of the main macroeconomic variables, most importantly hours, to news about future TFP increase. The main
characteristic of GHH preferences is that the optimal number of hours worked depends only on the contemporaneous
real wage, and therefore news about a future TFP increase produces neither substitution e¤ect, nor a wealth e¤ect
on hours. Consequently, hours do not decrease on impact as the result of news. This is not the case with KPR
preferences where the optimal number of hours worked responds to changes in lifetime income as well as the current
wage. Given good news about future changes in TFP, agents reduce today’s supply of labor, because they perceive
a higher level of lifetime income, and therefore want to enjoy more leisure.
26
and C2t : If the elasticity of substitution is greater than 1 in absolute value; goods are substitutes,
whereas, if the elasticity of substitution is less than 1 in absolute value, goods are complements.
Finally, I assume that the service ‡ow from the durable consumption good is proportional to the
stock of the durable consumption good St :
C2t = St ;
3.2
> 0:
Producers
Two …nal goods are produced in the economy: a perishable consumption good, produced in sector
1, and a capital good, produced in sector 2. A good produced in sector 2 can be used either as an
investment good in both sectors or as a consumer durable. Production processes in both sectors
require the use of labor and capital. In addition, the production function of sector 2 has inventories
as an argument.20 In both sectors, I model capital services as the product of the capital stock
and the level of capital utilization. The cost of increasing utilization is additional depreciation of
the capital stock. This feature is introduced through the depreciation rate that depends on the
rate of capacity utilization, and takes the form
j
j
0; 1,
j
2
j
(ujt ) =
j
0
+
j
1
(ujt
1) +
> 0 and j = 1; 2 corresponding to the two sectors. Parameter
state depreciation rate of the j
th sector, since
j
1
j
0
j
2
2
(ujt
1)2 ; where
represents the steady
is calibrated such that, in the steady state,
the utilization rate in both sectors is equal to one. Sector 1’s production technology is a standard
Cobb-Douglas function:
Y1t = F1t (K1t ; N1t ) = A1t (N1t )1
1
(u1t K1t )
1
;
where N1t and K1t represent labor and capital input at time t, u1t represents the rate of capacity
utilization in sector 1, A1t represents the technology process in sector 1, and 0 < 1
1
< 1 is
labor’s share in sector 1. Sector 2’s production function is assumed to have the form:
20
As Christiano (1988) argues: that "all other things being equal, larger inventory stocks probably do augment
society’s ability to produce goods. For example, spatial separation of the stages of production and distribution,
together with economies of scales in transportation, implies that labor inputs can be conserved by transporting
goods in bulk and holding inventories." Also, Kydland and Prescott (1982) suggest that "with larger inventories,
stores can economize on labor resources allocated to restocking." Therefore, adding inventories into the production
function does not seem unreasonable.
27
Y2t = F2t (K2t ; N2t ; It ) = A2t (N2t )1
2
2
(1
) (u2t K2t )
+ It
;
where N2t and K2t represent labor and capital used in the production of sector 2 output at time
t; u2t is the capacity utilization rate in sector 2, It denotes stock of inventories at time t; and
0<1
2
< 1 is labor’s share in sector 2. The parameter
production function of sector 2. If
controls the role of inventories in the
= 0 we are back to the standard Cobb-Douglas production
function case. Finally, the elasticity of substitution between capital and inventories is
elasticity is arguably less than one which is why
1
1+
; this
is required to be positive.21
Households are assumed to own the physical capital used in both sectors. Labor is assumed
to be mobile across sectors; at the same time, I assume that the adjustment cost is incurred when
the level of investment changes over time. In addition, changing stocks of consumer durables is
also subject to an adjustment cost.22 The capital stocks in both sectors, K1t and K2t , and the
stock of consumer durables St evolve over time following laws of motion:
K1;t+1 =
1
1
K2;t+1 =
1
2
St+1 = (1
(u1t ) K1t + X1t 1
1
(u2t ) K2t + X2t 1
2
S ) St
+ Dt 1
3
Dt
Dt 1
X1t
X1t 1
X2t
X2t 1
;
;
;
where X1t and X2t denote gross investment in sectors 1 and 2 at time t; while Dt denotes purchases
of new consumer durables. Function
j
( ) represents the adjustment cost function, which is chosen
so that it satis…es the condition of no adjustment costs in the steady state; i.e.
(j = 1; 2; 3) : Also,
0
j
( );
00
j
j
(1) =
0
j
(1) = 0,
( ) > 0: This function does not necessarily need to be identical across
the sectors, and, therefore, can take di¤erent forms.23
21
See Kydland and Prescott (1982).
I follow Bernanke (1985), Startz (1989), and Baxter (1996) in assuming that the stock of consumer durables is
subject to the adjustment cost, although my speci…cation is di¤erent from theirs.
23
See onliine Appendix C for the exact forms used.
22
28
3.3
Resource Constraints
Since an individual’s allocation of time is normalized to 1, the hours in both sectors cannot exceed
the total available hours Nt that are equal to 1
Lt ; where Lt denotes time allocated to leisure at
time t: Therefore, a unit of time is allocated as follows:
N1t + N2t + Lt
1:
The resource constraint for the sector producing the pure consumption good is
C1t
Y1t :
For the sector producing the capital good the resource constraint is
Dt + X1t + X2t +
3.4
It
Y2t :
Introducing News Shocks Into the Model
To analyze the theoretical e¤ects of news, I introduce news shocks into the model by making
reference to my estimates in Section 2. In particular, I assume that the news shock corresponds
to an aggregate news shock as identi…ed by my estimation procedure. I assume that the response
of TFP in model sector 1 corresponds to the response of TFP in the nondurables sector to an
aggregate news shock in the data. I assume that the response of TFP in model sector 2 corresponds
to the response of TFP in the durables sector to an aggregate news shock in the data. I …rst
estimate the regression coe¢ cients
P
k (k = 1; 2) : The sequence ni=0
0
js
k
i
in (1) ; in this case, Xt represents the productivity of sector
represents a point estimate of the impulse response function
of sector k 0 s TFP to a news shock (aggregate or sectoral), after n periods. In the regressions I set
J = 8 so that the implied impulse response functions of the levels of TFP in the two sectors are
constant for n > J = 8.
These estimated productivity responses are then introduced into the model. Figure 1 shows
the responses of sectoral TFPs to an aggregate news shock; the responses are smoother than
productivity processes commonly used in the theoretical news literature, where news about future
29
technology developments is often introduced as follows. The economy is assumed to be in the
steady state in period 0, when a signal arrives suggesting that in s periods a positive technology
shock will occur.24 In this case, the productivity process remains at its steady-state level until
period s, when the productivity increase is realized. TFP then rises by 1 percent and follows its
exogenous law of motion afterwards.25
In my analysis, the productivity process is at its steady state level in period 0, after which
it starts to increase, with TFP increasing by 1 percent in the long-run. In both approaches, in
period 0 households learn the expected future path of the technology process. The key di¤erence
is that in my analysis the productivity increase begins in period 1 and occurs smoothly over time,
whereas in the typical theoretical analysis it is delayed (s periods) and abrupt.
4
Calibration and the Estimation
Before obtaining quantitative predictions from the model, I assign numerical values to its parameters. I calibrate some of the structural parameters of the model in a standard fashion; the rest
of the parameters are estimated. Table 1 summarizes values of the calibrated parameters.
The time unit is de…ned to be a quarter. I assign a value of 0:9902 to the subjective discount
factor , which is consistent with an annual real interest rate of 4 percent. I calibrate utility parameters,
1
and
2;
such that the steady-state shares of nondurable goods and durable goods in com-
posite consumption equal the average over the sample period (C1 =C = 0:723 and C2 =C = 1
The preference parameter
0:723).
is chosen so that the agents allocate one-third of their time-endowment
to work. Following Bernanke (1985) and Baxter (1996), annual capital depreciation rates in the
two sectors are 7:1 percent; which leads to the quarterly depreciation rates,
1
0
and
2
0;
being 1:73
percent. The annual depreciation rate of the stock of durables is 15:6 percent (following Baxter(1996)). I calibrate the parameters
1
1
and
2
1
to ensure that steady-state capital utilizations in
both sectors, u1 and u2 ; equals unity. The labor share coe¢ cients, 1
1
and 1
2,
are chosen to
match the mean of labor’s share over the sample period. The parameter , which determines the
24
Christiano et al. (2010) and Jaimovich and Rebelo (2009), among others, allow for the possibility of this signal
to be false or noisy. That is, after s periods the expected increase in technology does not happen, or is smaller
than previously expected.
25
See, for example Christiano et al. (2010), Beaudry and Portier (2004), Beaudry and Portier (2005), Jaimovich
and Rebelo (2009), and Schmitt-Grohé and Uribe (2012).
30
role of inventories in the production function of sector 2, is chosen to match the share of inventories
in output. Finally, I choose the parameter
so that the elasticity of substitution between capital
services and inventories matches the value used by Christiano (1988).
TABLE 1: CALIBRATED PARAMETERS
Parameter Value
Description
1=4
1:04
Subjective discount factor
0:7
Service ‡ow from durables
1
1
0:74
Labor share in the nondurable goods sector
1
2
0:60
Labor share in the durable goods sector
1
0
0:0173
Steady-state depreciation rate in the nondurable goods sector
2
0
0:0173
Steady-state depreciation rate in the durable goods sector
S
0
0:0358
Depreciation rate of the stock of durables
0:0003
Determines the role of inventories in the production function
1
1:185
Composite consumption good parameter with sector 1
2
0:053
Composite consumption good parameter with sector 2
1
1
0:0303
Nondurable goods sector depreciation rate parameter
2
1
0:0247
Durable goods sector depreciation rate parameter
3:671
Elasticity of substitution between inventories and capital
I use impulse response function matching to estimate the remaining parameters:
(the inverse
of the elasticity of intertemporal substitution), h (the habit persistence parameter), % (the elasticity
of substitution between C1t and C2t ), the three coe¢ cients of the investment adjustment cost
functions ( 1 ;
and
2
2 ).
Let
2,
and
S ),
and the two coe¢ cients of the rate of capacity utilization functions (
denote parameters that I estimate,
1
2
( ) denote the model impulse responses that
are functions of the structural parameters , and ^ denote the corresponding estimated empirical
impulse responses. The estimator for
is the solution to the following minimization problem:
^ = arg min ^
0
( ) W
1
^
( ) ;
where W is the diagonal matrix with the sample variances of the ^ 0 s along the diagonal.26 I match
26
I follow Altig et al. (2011) who argue that with this choice of the weighting matrix W; ^ is the value of
31
which
the following impulse response functions: composite consumption, aggregate hours, output, and
investment in the durable goods sector. The point estimates of the parameters are given in Table
2. In the following section, I discuss the predictions of the model.
TABLE 2: ESTIMATED PARAMETERS
Parameter Estimated Value Description
5
1
9:48
Sector 1 investment adjustment cost function parameter
2
5:31
Sector 2 investment adjustment cost function parameter
S
8:73
Stock of durables adjustment cost function parameter
1:64
Intertemporal elasticity of substitution
h
0:78
Habit persistence in consumption parameter
%
0:91
Elasticity of substitution
1
2
0:17
Parameter of the depreciation rate in the nondurable sector
2
2
0:14
Parameter of the depreciation rate in the durable sector
Predictions of the Estimated Model
One of the main challenges the news literature has faced is building a model that can generate
Pigou cycles, a comovement between consumption, hours, output, and investment, in response to
news about higher future TFP. Beaudry and Portier (2004) were the …rst authors to recognize
that the standard real business cycle model, with KPR preferences, fails to meet this challenge.
In particular, good news increases consumption and leisure on impact through the wealth e¤ect.
Since leisure increases, hours worked and output decrease. The only way for consumption and
hours (or output) to move in opposite directions is through a decrease of investment. To solve
this problem, Beaudry and Portier propose a three-sector model, in which consumption is given
as a composite of nondurable and durable goods. Both of these goods are produced with labor
and a …xed production factor. The model is capable of generating Pigou cycles. However, in
a more recent paper, Jaimovich and Rebelo (2009) formulate a one-sector model that is able to
generate Pigou cycles. This is a standard real business cycle model, augmented with the investment
adjustment costs and variable capital utilization. Furthermore, the model features a new type of
ensures that theoretical IRFs lie as much as possible inside the con…dence bands of estimated IRFs.
32
preferences that do not induce a wealth e¤ect on leisure/labor when news is received. Therefore,
hours does not decrease on impact and the desired comovement between output, consumption
and investment can be obtained. Several other authors have been able to obtain the desired
comovement between these variables using a one-sector model (see Den Haan and Kaltenbrunner
(2009), Christiano et al. (2010), Schmitt-Grohé and Uribe (2012). In most of these papers news is
introduced as described above: in period t agents learn that there will be a one-percent permanent
increase in TFP beginning in period t + j, where 0 < j
n. Therefore, the productivity process
features a kink in period t + j.
In my empirical analysis I make a distinction between the durable and nondurable goods
sectors. One obvious di¤erence between the producers in these two sectors is the possibility of the
durable sector producers holding stocks of inventories. This channel can help my model replicate
comovement between consumption and investment, since holding stocks of inventories is one way
that the durable goods sector producers can meet higher consumer demand without necessarily
having to decrease investment.
Finally, there are two main distinctions between my approach and the approaches taken in the
aforementioned papers. First, as indicated before, I introduce news shocks by feeding the empirical
responses of TFPs in the two sectors into the model. Thus, the productivity process in this case
does not feature a kink, but is rather a much smoother process. Second, the focus of my analysis is
not only on obtaining the right qualitative comovement between the main macroeconomic variables
(hours, consumption, output and investment), but also on obtaining quantitatively good …t of the
model impulse response functions to those in the data, while considering additional implications
of the model for the behavior of inventories, and behavior of sectoral level data. In order to make
progress on these quantitative dimensions, it was necessary to use a richer model than the ones
found in the literature.
5.1
Benchmark Model
Figures 13 and 14 display the theoretical and empirical responses of …ve macroeconomic time
series (consumption, hours, investment, output and inventories-to-sales ratio) to a unit aggregate
news shock. Theoretical responses are computed using the benchmark model described in Section
3. The shaded areas represent 90% con…dence intervals of the empirical responses, and the dashed
33
lines represent point estimates of the empirical impulse responses. The solid lines represent theoretical responses under GHH preferences, and the starred lines represent responses under KPR
preferences. There is no signi…cant di¤erence between the model responses when preferences take
the KPR or GHH form. This result is not surprising, considering the nature of the technology
process. In particular, the technology process does not feature the kink as it does in the most
of the rest of the theoretical literature on news shocks; instead, it starts increasing slowly from
period 1. This representation of technology is more consistent with the notion that the technology
process di¤uses slowly over time, and, therefore, the main distinction between KPR and GHH
preferences described above is almost eliminated.
FIGURE 13: Model and Empirical Responses to a unit Aggregate News Shock
Consumption and Hours Responses
Note: The shaded areas represent 90% con…dence intervals of the empirical responses, and the dashed
lines represent point estimates of the empirical impulse responses. The solid lines represent theoretical
responses under GHH preferences, and the starred lines represent responses under KPR preferences.
Comovement between total hours, consumption, output, and investment is evident. Aggregate
hours worked increase; at the same time, the benchmark model is not able to match the response
of hours worked in the nondurable sector. In particular, the benchmark model wrongly predicts
34
a decrease of nondurable hours. My intuition is as follows: hours can move freely between the
sectors, and, therefore, hours worked tend to increase in the sector in which the productivity is
higher, which is the durable sector. In order to solve this problem, in one variant of the model
I introduce adjustment costs in labor in the nondurable sector. Adding this feature improves
the model …t in this dimension; the model can generate an increase of hours in the nondurable
goods sector.27 Moreover, the model matches the response of hours in the durable goods sector
quite well. Since this increase is larger than the decrease of hours in the nondurables sector, the
benchmark model is still able to obtain increase of the total hours. However, the model needs a
labor adjustment cost in order to be able to generate more realistic responses of the nondurable
sector hours.
The model does a good job in replicating the consumption responses. It can generate positive initial responses of consumption in the durable goods sector and in composite consumption,
whereas the initial response of nondurable consumption is below the con…dence bands for several periods. The response of durable goods consumption lies inside the con…dence bands in all
periods. The estimate of the parameter of the elasticity of substitution suggests some degree of
complementarity between durable and nondurable goods in consumption, which helps obtaining
comovement between consumptions in the two sectors.
The model cannot generate a negative initial response of investment in the nondurable goods
sector, which is observed in the data. In order to drive down investment in the nondurable sector,
a high value of the coe¢ cient in the investment adjustment cost function is needed. This is also
true in the case of durable goods sector investment; the estimated investment adjustment cost
must be quite large. Had these adjustment costs not been introduced, the responses would be
much larger and occur more quickly, because changing the level of investment would not be costly
for producers. The response of output in the durable goods sector is matched very well; the model
response of durables sector output lies within the 90% con…dence bands of the empirical response
almost all the time, whereas nondurables sector output is inside the con…dence bands only in
the longer run. That is, the hump- shaped response of output in the nondurable goods sector
cannot be obtained, which is primarily the result of the qualitative response of output following
the shape of the productivity process in the nondurable sector. Rather than being hump-shaped,
27
Also Jaimovich and Rebelo (2009) introduce this cost in order to obtain better response of the total hours.
35
the response of nondurable goods sector output is very small over the …rst four quarters, after
which it starts slowly to increase, reaching the con…dence band of the empirical response after six
quarters.
Finally, the model is able to replicate the response of the inventories-to-sales ratio, which is
not one of the responses that is being matched in the estimation. That my model works well in
this dimension is very encouraging, particularly since it is able to replicate the response of the
variable which, as mentioned above, is relevant for understanding di¤ering extent to which news
shocks are propagated in durable and nondurable goods sectors.
FIGURE 14: Model and Empirical Responses to a unit Aggregate News Shock
Note: The shaded areas represent 90% con…dence intervals of the empirical responses, and the dashed
lines represents point estimates of the empirical impulse responses. The solid lines represent theoretical
responses under GHH preferences, and the starred lines represent responses under KPR preferences.
I conclude by arguing that by examining a model with distinct durable and nondurable goods
sectors, with an explicit role for inventories, and by modeling news shocks using an approach that
departs from most of the theoretical literature, I am able to replicate some of the key characteristics
of the empirical responses of the economy to news about future productivity. The benchmark
model performs relatively poorly in explaining the behavior of the nondurable goods sector hours,
36
but is quite successful in explaining the behavior of the durable goods sector and some aggregate
variables.
6
Conclusions
In this paper, I present evidence that the responses to news shocks of the fundamentals in the
durable goods sector are di¤erent from the responses of these fundamentals in the nondurable goods
sector. In particular, the responses of durable goods sector fundamentals are signi…cantly greater
than the responses of nondurable goods sector fundamentals. After a 1 percent aggregate news
shock, durable sector productivity rises by approximately 3 percent after ten quarters, whereas
the response of productivity in the nondurable goods sector is approximately 0:5 percent. The
percentage responses of other durable goods sector fundamentals are also signi…cantly higher than
those of the same fundamentals in the nondurable goods sector. This empirical evidence suggests
that aggregate news shocks are propagated through the durable goods sector of the economy. In
order to explain these di¤erent behaviors of the durable and nondurable goods sectors, I introduce
inventories into the analysis. By looking at the behavior of this variable, which has been largely
neglected in the news literature, I am able to conclude that inventories play an important role in
how aggregate news shocks are propagated through the durable goods sector.
As a theoretical framework, I use a two-sector, two-factor, real business cycle model. I also
introduce inventories into the production function of durable goods producers. My model is
consistent with the empirical evidence on how the economy responds to news shocks. Speci…cally,
the model is successful in mimicking the empirical responses to news shocks at the sectoral level.
First, the model reproduces the comovement among hours, consumption, output and investment
in both sectors. Second, the model is able to reproduce the stronger overall response of the durable
goods sector to news shocks. Finally, the model is able to perfectly match inventories responses.
37
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